We present a combinatorial solution to the problem of determining the number of lozenge tilings of a hexagon with sides a, b + 1, b, a + 1, b, b + 1, with the central unit triangle removed. For a = b, this settles an open problem posed by Propp 7]. Let a, b, c be positive integers, and denote by H the hexagon whose side-lengths are (in cyclic order) a, b, c, a, b, c and all whose angles have 12...

We present the theoretical approach to study the unconventional Josephson junction (uJJ) made by putting the non-superconducting strip on the top of superconducting strip. We work in the framework of the Ginzburg-Landau, Bogoliubov de Gennes and Usadel equations. Then we solve the non-linear partial differential equations numerically for few simple cases. We review the similarities and new aspe...

Many questions on special values of L-functions are tied to the study of period integrals of automorphic forms. A notable example is the formula of Waldspurger ([22]) that relates the toric period on GL2 or its inner form to some central critical L-value. The conjecture of Gan, Gross and Prasad ([4]) started with the Gross-Prasad conjecture ([5]), as well as the refinement of Ichino and Ikeda (...

SAE (The Society of Automotive Engineers) tarafından düzenlenen resmi bir proje yarışması olan Formula Stu-dent, dünya çapında birçok üniversite öğrencilerinin kendi bilgi birikimlerini kullanarak belirlenen kurallara uygun şekilde tipi yarış arabası tasarlamasını amaçlayarak, öğrencilerin otomotiv sahasındaki bilgilerini geliştirmelerine imkan tanımaktadır. Bu çalışmada SolidWorks 2018 program...

Both the quality of the results of TEX s formula layout algorithm and the complexity of its description in the TEXbook are hard to beat The algorithm is verbally described as an imperative program with very complex control ow and complicated manipulations of the data structures representing formulae In a forthcoming textbook we describe TEX s formula layout algorithm as a functional program tra...

In a recent paper we showed that the electroweak chiral Lagrangian at leading order is equivalent to the conventional [Formula: see text] formalism used by ATLAS and CMS to test Higgs anomalous couplings. Here we apply this fact to fit the latest Higgs data. The new aspect of our analysis is a systematic interpretation of the fit parameters within an EFT. Concentrating on the processes of Higgs...